Let us take a first look into the simplest BSM realization of (fast) neutrino decays, which is of the form \(\nu _i \rightarrow \nu _j \phi /Z^{\prime }\) .
Here and in the following we will denote with \(\nu _i,\nu _j\)  active neutrino mass eigenstates and with \(\nu _4\)  the newly introduced sterile neutrino.
Angular momentum conservation requieres the end product of the active neutrino decay to contain a scalar (\(\phi \) ) or vector (\(Z^{\prime }\) ) boson.
Assuming that the exemplary decay is fast allows us to plot in figure REF  the actual physical mass of the active neutrino against the one which would be inferred from cosmological measurements [1]}.
In the stable neutrino scenario the correspondence between both masses is one to one, represented by the black dashed line.
In contrary in the decaying neutrino scenario the physical neutrino mass is generically higher than the cosmological one and the actual relationship depends on the active neutrino hierarchy and is dictated purely by energy and angular momentum conservation.
In particular this can become important if future experiments as DESI & EUCLID do not detect neutrino masses as this would contradict the classical normal and inverted hierarchy interpretation, whereas decaying neutrinos can bring both results and interpretation in accordance.
